A theoretical evaluation of chemical ordering and glass transition in liquid Mg-Sb alloys
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I.
INTRODUCTION
A thorough understanding of the factors affecting the glassforming ability (GFA) of alloys is still lacking although many empirical rules have been proposed over the last decade. It has often been suggested that there is a strong correlation between GFA and the state of chemical order in the melt; see, for example, Sommer. 1 In a recent study 2 the present authors analyzed the Mg-Sn system in terms of thermodynamic models for the individual phases. The basic idea was to calculate various properties at large undercoolings from the models. Special attention was paid to the isentropic temperature, the nucleation temperature, and the To temperature. In the present report we continue that work by applying the same approach to the Mg-Sb system. This choice may seem unexpected because the Mg-Sb phase diagram, which was recently assessed by Nayeb-Hashemi and Clark, 3 does not have any of the typical features of a glassforming system, e.g., deep eutectics. On the contrary, instead of a deep eutectic it has an intermediate phase, Mg3Sb2, with a melting point 600 K above the melting points of pure Mg and Sb. The reason for studying this sytem is that one would expect both a strong tendency for chemical order and a high isentropic temperature in liquid alloys close to the Mg3Sb2 composition. II.
E X T R A P O L A T I O N OF T H E LIQUID PHASE TO LARGE UNDERCOOLINGS; THE ISENTROPIC T E M P E R A T U R E
It was pointed out by Kauzmann 4 that some information indicates that the liquid state would obtain a lower entropy than the crystalline phase below some temperature well above zero. This is often called the Kauzmann paradox and that temperature is called the isentropic temperature. It is generally believed that this situation is avoided by th~ occurrence of the glass transition. In the glassy state below the glass transition, Cp is believed to approximate Cp of the crystalline phase and the entropy at the absolute zero would not take a negative value, but approach zero. A method of evaluating a lower limit for the glass transition temperature would thus be to extrapolate the properties of the liquid BJORN JONSSON and JOHN ~-GREN are with the Division of Physical Metallurgy, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted September 29, 1986 METALLURGICALTRANSACTIONS A
phase to lower temperatures and evaluate where its entropy equals the entropy of the stable crystalline state. The idea is that the amorphous phase would there change its character from liquid to glassy by a second or higher order transition, i.e., without a discontinuous change in entropy. Unfortunately, the extrapolation from the stable region of the liquid and down to the isentropic temperature is usually very long and uncertain. In the general case it is thus impossible to predict the isentropic temperature by such an extrapolation. On the other hand, the convention that there is an isentropic temperature can be used to support the extrapolation of the properties of the liquid phase below the liquidus tempera
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